import heapq as hq
import math
from collections.abc import Iterator




class 					_UpperCAmelCase			:



 '''simple docstring'''




 def __init__(		self				:   Dict							, lowercase_				:   Optional[Any])						->	List[Any]:


   """simple docstring"""







   _UpperCamelCase           =    str(id_)
   _UpperCamelCase           =    None
   _UpperCamelCase           =    None
   _UpperCamelCase           =    []
   _UpperCamelCase           =    {}  # {vertex:distance}







 def __lt__(		self				:   List[str]							, lowercase_				:   Union[str, Any])						->	Optional[int]:


   """simple docstring"""







   return self.key < other.key







 def __repr__(		self				:   List[Any])						->	Tuple:


   """simple docstring"""







   return self.id







 def 		__UpperCAmelCase				(		self				:   List[Any]							, lowercase_				:   int)						->	Union[str, Any]:


   """simple docstring"""







   self.neighbors.append(lowercase_)







 def 		__UpperCAmelCase				(		self				:   Optional[Any]							, lowercase_				:   int							, lowercase_				:   List[Any])						->	List[Any]:


   """simple docstring"""







   _UpperCamelCase           =    weight


def 				lowerCAmelCase__       (			a__    ,     a__    ,     a__    ,     a__ )      ->str:




  '''simple docstring'''

  graph[a - 1].add_neighbor(graph[b - 1] )
  graph[b - 1].add_neighbor(graph[a - 1] )
  # add the edges:
  graph[a - 1].add_edge(graph[b - 1]    ,     a__ )
  graph[b - 1].add_edge(graph[a - 1]    ,     a__ )


def 				lowerCAmelCase__       (			a__    ,     a__ )      ->list:




  '''simple docstring'''

  _UpperCamelCase           =    []
  for u in graph:
    _UpperCamelCase           =    math.inf
    _UpperCamelCase           =    None
  _UpperCamelCase           =    0
  _UpperCamelCase           =    graph[:]
  while q:
    _UpperCamelCase           =    min(a__ )
    q.remove(a__ )
    for v in u.neighbors:
      if (v in q) and (u.edges[v.id] < v.key):
        _UpperCamelCase           =    u
        _UpperCamelCase           =    u.edges[v.id]
  for i in range(1    ,     len(a__ ) ):
    a.append((int(graph[i].id ) + 1, int(graph[i].pi.id ) + 1) )
  return a


def 				lowerCAmelCase__       (			a__    ,     a__ )      ->Iterator[tuple]:




  '''simple docstring'''

  for u in graph:
    _UpperCamelCase           =    math.inf
    _UpperCamelCase           =    None
  _UpperCamelCase           =    0

  _UpperCamelCase           =    list(a__ )
  hq.heapify(a__ )

  while h:
    _UpperCamelCase           =    hq.heappop(a__ )
    for v in u.neighbors:
      if (v in h) and (u.edges[v.id] < v.key):
        _UpperCamelCase           =    u
        _UpperCamelCase           =    u.edges[v.id]
        hq.heapify(a__ )

  for i in range(1    ,     len(a__ ) ):
    yield (int(graph[i].id ) + 1, int(graph[i].pi.id ) + 1)


def 				lowerCAmelCase__       (			)      ->None:




  '''simple docstring'''



if __name__ == "__main__":
   import doctest

   doctest.testmod()





from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


lowerCamelCase__  =					{
    '''configuration_longformer''': [
        '''LONGFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''LongformerConfig''',
        '''LongformerOnnxConfig''',
    ],
    '''tokenization_longformer''': ['''LongformerTokenizer'''],
}

try:
   if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   lowerCamelCase__  =					['''LongformerTokenizerFast''']

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   lowerCamelCase__  =					[
       '''LONGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST''',
       '''LongformerForMaskedLM''',
       '''LongformerForMultipleChoice''',
       '''LongformerForQuestionAnswering''',
       '''LongformerForSequenceClassification''',
       '''LongformerForTokenClassification''',
       '''LongformerModel''',
       '''LongformerPreTrainedModel''',
       '''LongformerSelfAttention''',
   ]

try:
   if not is_tf_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   lowerCamelCase__  =					[
       '''TF_LONGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST''',
       '''TFLongformerForMaskedLM''',
       '''TFLongformerForMultipleChoice''',
       '''TFLongformerForQuestionAnswering''',
       '''TFLongformerForSequenceClassification''',
       '''TFLongformerForTokenClassification''',
       '''TFLongformerModel''',
       '''TFLongformerPreTrainedModel''',
       '''TFLongformerSelfAttention''',
   ]


if TYPE_CHECKING:
   from .configuration_longformer import (
       LONGFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
       LongformerConfig,
       LongformerOnnxConfig,
   )
   from .tokenization_longformer import LongformerTokenizer

   try:
      if not is_tokenizers_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .tokenization_longformer_fast import LongformerTokenizerFast

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_longformer import (
          LONGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
          LongformerForMaskedLM,
          LongformerForMultipleChoice,
          LongformerForQuestionAnswering,
          LongformerForSequenceClassification,
          LongformerForTokenClassification,
          LongformerModel,
          LongformerPreTrainedModel,
          LongformerSelfAttention,
      )

   try:
      if not is_tf_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_tf_longformer import (
          TF_LONGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
          TFLongformerForMaskedLM,
          TFLongformerForMultipleChoice,
          TFLongformerForQuestionAnswering,
          TFLongformerForSequenceClassification,
          TFLongformerForTokenClassification,
          TFLongformerModel,
          TFLongformerPreTrainedModel,
          TFLongformerSelfAttention,
      )

else:
   import sys

   lowerCamelCase__  =					_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)




